As a summary, we note that all of the additional errors resulting from crosstalk in the MS gate, except for Eq. (REF ), yield a negligibly-small contribution. They are either due to the dephasing (REF ), which is often negligible for the short duration of the MS gate, or they are proportional to the already-small error rate of the MS-gate weighted by the additional small pre-factor (REF ). Accordingly, the leading source of crosstalk errors will stem from the coherent contribution in Eq. (REF ). The present error model is useful to make a quantitative comparison of the shuttling-based versus static-string performance of the QEC protocols discussed in Ref. [1]}, assessing quantum logic advantage with both approaches by a microscopic description of the errors on the same footing.
